When we think of Orson Welles and television, the impulse is often to smirk. The innumerable talk-show appearances, though reliably entertaining, couldn't help but seem sad in comparison to his earlier triumphs. And those ads for the likes of Findus frozen foods and Paul Masson wine were hard to take seriously even before viral video made us familiar with Welles's absurd on-set relationship with hack copy, which ranged from perfectionist quibbling to ostensibly drunken slurring.

Fair enough. Such undertakings could hardly be counted among the highlights of any career, let alone one that included Citizen Kane and Chimes at Midnight. But it's worth bearing two things in mind in between chuckles. First, the proceeds from these appearances were invariably funnelled toward one or other of the vibrant creative personal projects to which Welles remained doggedly committed until his dying day, even as they became harder and harder to realise; in this respect, they took the place of cameo movie appearances in his unorthodox personal economy. And second, there was a point at which Welles seemed on the brink of creatively revolutionising television as he had theatre, radio and film.

The nascent medium had piqued the artist's interest after the war but he decamped for Europe in 1947, the year before television took root in the United States. He kept tabs on its development and, in 1953, the year it broke through in the UK, he briefly returned to the US to star in a rapturously received version of King Lear, directed by Peter Brook for CBS. In 1955, back in London, he got his the opportunity to flex his own creative muscles before the TV camera in Orson Welles' Sketchbook, six 15-minute monologues for the BBC, which are being repeated as part of BBC Four's Welles season this Christmas.

Although famous as a large actor in every sense, Welles was always more comfortable as a storyteller than performing in character, and in television he felt he had found an ideal platform. He saw it not as a vehicle for spectacle like film or theatre, but as a conversational form like radio, perfect for his preferred role of hands-on narrator or personalised chorus, mediating between audience and tale.

The Sketchbook testifies to this sensibility: addressing the camera directly, Welles makes eye contact with his viewers as he holds forth on subjects ranging from "the precious gift of stage fright" to state interference in private life, all the while doodling illustrative sketches on a pad. He fosters an intimate, even conspiratorial tone that makes him an impeccable embodiment of the medium's proverbial status as a guest in the front room – Peter Ustinov meets Rolf Harris, perhaps. To our digitally accustomed eyes, the one-to-one timbre of the programme comes off like a monochrome forebear of Skype or YouTube.

Even at this relatively young age – he turned 40 during the show's run – Welles was accustomed to anecdotalising his early career, touching at various points on his teenage debut at Dublin's Gate Theatre, his sensational "voodoo Macbeth" production in Harlem and the notorious War of the Worlds radio broadcast. (A dinner party on Long Island, he reported, was kept up to speed on events by the butler, who delivered such politely apocalyptic nuggets as "I believe it's interplanetary, sir.")

Welles gives one episode over to a delightful version of the story of Bonito, a young bull befriended by a boy before being sent to the corrida, which was once intended to form part of It's All True, the famously abandoned South American documentary project that the film-maker undertook after The Magnificent Ambersons. This is perhaps the closest we'll ever get to an idea of his intentions.

But Welles covers a promiscuous range of other subjects too, glancing at Houdini and Rasputin, autocues and witch-doctors. The final episode concerns the expansion and abuse of bureaucratic and police powers; anticipating Charlton Heston's Vargas in Touch of Evil, he insists that "it's the [nature] of a policeman's job that it should be hard".

The Sketchbook went down well, and a few months later Welles began a series of ITV travelogues recorded throughout Europe that greatly expanded his – indeed, everyone's – televisual grammar. Shot in locations ranging from Chelsea to Paris, Vienna to the Basque country, Welles proved a sharp but humble interviewer and boldly experimented with over-the-shoulder shots and "noddies" (response shots recorded separately from an interview then interwoven with the subject's answers), as well as location shooting, synchronised sound recording and handheld crime recreations. Although factually based, these were still a kind of storytelling, in the manner of personal essays.

The following year, back in the US, he teamed up with Lucille Ball and Desi Arnaz's production company to make a half-hour studio-shot story, The Fountain of Youth, which remains a radical masterpiece of television art. A playful and macabre distillation of his ideas about TV as a nimble storyteller's medium, it placed Welles in the thick of his story, deploying still photographs and illustrations, on-camera set changes and tricksy sound mixing to adorn a wry tale about vanity and ageing.

For convoluted reasons, the pilot was shelved and Welles's chance of conquering the medium passed. He would sporadically work in TV again as a creator rather than performer-for-hire; near the end of his life, for instance, he made a pilot for a talk show of his own and devised a King Lear specifically for the straight-to-video market. Neither was commissioned. But his televisual grammar is still evident in his widely known work. F for Fake, conceived for TV and hailed on its theatrical release as a new form – the essay film! – was in fact of a piece with his 50s travelogues, a personalised take on a broad subject, illustrated from a subjective sensibility. It was a little like a sketchbook.

• Orson Welles' Sketchbook start on BBC Four on 18 December. Ben Walters is the author of Orson Welles (Life and Times). He writes in detail about The Fountain of Youth here.